Lachlan passed away in January 2010. As a memorial, this site remains as he left it.Therefore the information on this site may not be current or accurate and should not be relied upon.
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"Briefly, an "ant" moves around on an infinite checkerboard, each square of which we refer to as a "cell". Each cell in the plane is labeled as either an L-cell or an R-cell
(usually, one fills the plane with L-cells to start). The ant starts out on the boundary between two cells, and as it passes through each cell, it makes a 90 degree turn,
turning to the left in L-cells and to the right in R-cells, and it changes the state of the cell it just left, switching L-cells to R-cells, and vice versa. Following this simple set
of rules gives rise to some rather complicated behavior; the pattern of the ant's track alternates between apparent chaos and symmetry, and eventually it starts to build a
"highway" moving off in a single direction.

The above described ant (and some variations) was originally studied by Chris Langton (then at the Santa Fe Institute, more recently a co-founder of the Swarm
Corporation). Later, Jim Propp generalized the ant by considering each cell to be in one of n different states: each ant has some "internal programming" which tells it
whether to turn left or right when the cell is in that state. This "program" can be represented as a string of n Ls and Rs, and the kth letter represents the ant's action
when it comes to a cell in state k. For example, Langton's ant, described above, is a 2 state ant with the rule string LR (or in binary 10, so we call this "ant number 2").
The 7 state ant with rule string LLRRRLR (ant number 98) turns left when it visits a cell in state 1, 2, or 6, and right when it visits cells in state 3, 4, 5, or 7.

For all such generalized ants, one can readily see that if there is at least one L and at least one R in the rule string, the track of the ant will always be unbounded. And
certain ants exhibit recurrent symmetry, while others have apparently chaotic behavior. "

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